AN IDEAL-BASED ZERO-DIVISOR GRAPH OF 2-PRIMAL NEAR-RINGS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 6, 2009, pp.1051-1060
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.6.1051

Title & Authors

AN IDEAL-BASED ZERO-DIVISOR GRAPH OF 2-PRIMAL NEAR-RINGS

Dheena, Patchirajulu; Elavarasan, Balasubramanian;

Dheena, Patchirajulu; Elavarasan, Balasubramanian;

Abstract

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact -subspace. We also study the zero-divisor graph (R) with respect to the completely semiprime ideal I of N. We show that (R), where is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph (R).

Keywords

graph;prime ideal;2-primal;Zariski topology and cycle;

Language

English

Cited by

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